82144 ÷ 6 = 13690 R4
Alright, let's work through the division of 82144 by 6 step by step.

Step 1:
6 goes into 8 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 8 to get 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 6

Step 2:
6 goes into 22 3 times with a remainder of 4.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 18 from 22 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 6

Step 3:
6 goes into 41 6 times with a remainder of 5.
Write down 6 as next digit of of the result. 
Result so far: 136
Subtract 36 from 41 to get 5.
Bring next digit (4) of the dividend behind the 5 and repeat the process: 54 / 6

Step 4:
6 goes into 54 9 times with a remainder of 0.
Write down 9 as next digit of of the result. 
Result so far: 1369
Subtract 54 from 54 to get 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 6

Step 5:
6 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 13690
Subtract 0 from 4 to get 4.

The final result is 13690 with a remainder of 4.